We present a Search and Matching model with heterogeneous workers (entrants and incumbents) that replicates the stylized facts characterizing the US and the Spanish labor markets. Under this benchmark, we find the Post-Match Labor Turnover Costs (PMLTC) to be the centerpiece to explain why the Spanish labor market is as volatile as the US one. The two driving forces governing this volatility are the gaps between entrants and incumbents in terms of separation costs and productivity. We use the model to analyze the cyclical implications of changes in labor market institutions affecting these two gaps. The scenario with a low degree of workers' heterogeneity illustrates its suitability to understand why the Spanish labor market has become as volatile as the US one.